There are two possible sections of the book that you might be referring to. Chapter 5 is when Winnie first meets Jesse Tuck and she happens to come across him as he is drinking from the spring. Winnie asks Jesse if she may have a drink because she is really thirsty. This is how Jesse responds: "You mustn't drink from it. Comes right up out of the ground. Probably pretty dirty." Winnie keeps insisting that she be allowed to take a drink and Jesse keeps dancing around the issue by saying that it would be bad for her to drink any of it. So the reason that Jesse gives Winnie is that the water is dirty and wouldn't be good for her.
He is lying of course because he knows that the water would give Winnie immortality.
Later in chapter 14 Jesse asks Winnie to not drink from the water for a different reason. Jesse wants Winnie to wait until she is 17 years old before taking a drink. That would put her at the same age as Jesse was when he took a drink. Jesse says that they would then be the same age and could go away together. "We could get married, even. That'd be pretty good, wouldn't it!" So the second reason Jesse gives Winnie is to wait in order that they can be the same starting age for the rest of eternity.